A4: Activities on Vertical Launch with Air Resistance
Place the ball at (x,y) = (10,40) m. This point will be referred to as the "launch point."
Make the following settings for the ball (see the figure below).
vx (0) = 0, vy (0) = 20.0 m/s
C = 0.009 kg/m,
m= 0.1 kg; the
last one is set automatically when you load the applet.
Launch the ball, and observe how
the velocity and
acceleration vary in time. Also observe the x and y components and magnitude of the velocity (speed) as displayed in the control
panel. Then answer the following questions.
Part 1
1. During the motion, the x-component
of the velocity vector of the ball is 0 at all times and the y-component is
(a) decreasing on the way up, 0 at the top, and decreasing uniformly
on the way down
(b) decreasing on the way up, 0 at the top, and increasing uniformly on the way down
(c) decreasing on the way up, 0 at the top, and decreasing on the way down, but more and more slowly and approaching
a constant value
(d) decreasing on the way up, 0 at the top, and increasing on the way down, but more and more slowly and approaching
a constant value
2. During the motion, the x-component of the acceleration vector of the ball is 0 at all times and the y-component is
(a) positive on the way up, 0 at the top, and negative and constant on
the way down
(b) negative on the way up, 0 at the top, and negative and constant on the way down
(c) positive on the way up, positive at the top, positive on the way down but approaching 0
(d) negative on the way up, negative at the top, negative on the way down but approaching 0
3. The ball's acceleration when the ball is leaving the launch point, when it is at the top, and when it is returning to the launch point has
(a) the same magnitude at all three instants
(b) has the same magnitude when the ball leaves from and returns to the launch point, but a different magnitude
at the top
(c) different magnitudes at all three instants
4. The ball's acceleration when the ball is leaving the launch point, when it is at the top, and when it is returning to the launch point
(a) has the same direction at all three instants
(b) has the same direction when the ball leaves from and returns to the launch point, but the direction is undefined
at the top because the acceleration is zero at this point
(c) has different directions when the ball leaves from and returns to the launch point
5. Calculate the magnitude of ball's acceleration due to air resistance at the launch point, at the top, and when it returns to the launch point. Hint: Use the equations in the "Lesson on Air Resistance" under Applet Help in the applet's Help menu.
6. Calculate the magnitude of the ball's net acceleration at the launch point, at the top, and when it returns to the launch point.
7. Compare the times elapsed while the ball is moving from the launch point up to the top and while the ball is moving from the top back down to the launch point. The time for upward motion of the ball is
(a) equal to the time for downward motion
(b) less than the time for downward motion
(c) greater than the time for downward motion
8. Explain your observation in Item 7 by considering the ball's acceleration on the way up and on the way down and the corresponding behaviour of the ball's velocity as a function of time. Exact equations are not required to explain the observation.
Part 2
From your activities in the previous part you will have gathered the following point. As the ball is falling back down from the top, its speed increases from 0 but approaches a constant value. This constant value is known as terminal speed and the corresponding velocity is called terminal velocity. Now answer a few questions about the terminal speed/velocity.
9. As the ball's speed approaches terminal speed, the ball's acceleration
(a) approaches 0
(b) approaches a constant that is non-zero
(c) does not approach a constant
10. Calculate the terminal speed of the ball for the settings given at the very beginning of these activities.
Digging Deeper
11. If you double the initial velocity of the ball, the terminal velocity of the ball will
(a) quadruple because the magnitude of the acceleration due to air resistance will
quadruple
(b) double because the magnitude of the acceleration due to air resistance will double
(c) will remain the same because the terminal velocity is independent of the initial velocity for a given object.
(d) halve because the magnitude of the acceleration due to air resistance will double
(e) be reduced to one fourth because the magnitude of the acceleration due to air resistance will quadruple
12. If you double the mass of the ball without changing the initial velocity, will the terminal velocity of the ball change? If yes, what the new value will be?